A source of sonic oscillation with frequency `n_0=600Hz` moves away and at right angles to a wall with velocity `u=30(m)/(s)`. A stationary reciever is located on the line of source in succession wall`rarr`source`rarr`receiver. If velocity of osund propagation is `v=330(m)/(s)`, then
Q. The wavelength of reflected waves received by the receiver is

Options

A. beats frequency recorded by the receiver is 110 Hz
B. wavelengths of direct and reflected waves received by the receiver are 50 and 60 cm respectively
C. if receiver stands in between wall and source, beats recorded by the receiver is 0
D. if receiver stands between wall and source, then wavelengths of direct and reflected waves are 60 cm each

Explanation

To solve the problem step by step, we will follow the principles of wave motion and the Doppler effect.

### Step 1: Identify the given data
- Frequency of the source, \( n_0 = 600 \, \text{Hz} \)
- Velocity of the source moving away from the wall, \( u = 30 \, \text{m/s} \)
- Velocity of sound, \( v = 330 \, \text{m/s} \)

### Step 2: Calculate the frequency of the reflected sound wave
When the source moves away from the wall, the frequency of the sound wave reflected back to the source can be calculated using the formula for the Doppler effect:

\[ n_r = n_0 \frac{v}{v + u} \]

Substituting the values:

\[ n_r = 600 \, \text{Hz} \times \frac{330 \, \text{m/s}}{330 \, \text{m/s} + 30 \, \text{m/s}} \]

### Step 3: Simplify the equation
Calculate the denominator:

\[ n_r = 600 \, \text{Hz} \times \frac{330}{360} \]

### Step 4: Perform the calculations
Now, simplify the fraction:

\[ n_r = 600 \, \text{Hz} \times \frac{11}{12} \]

Calculating this gives:

\[ n_r = 600 \times 0.9167 \approx 550 \, \text{Hz} \]

### Step 5: Calculate the wavelength of the reflected waves
The wavelength \( \lambda \) of the reflected waves can be calculated using the formula:

\[ \lambda = \frac{v}{n_r} \]

Substituting the values:

\[ \lambda = \frac{330 \, \text{m/s}}{550 \, \text{Hz}} \]

### Step 6: Perform the final calculation
Calculating this gives:

\[ \lambda = 0.6 \, \text{m} \]

### Step 7: Convert to centimeters
To express the wavelength in centimeters:

\[ \lambda = 0.6 \, \text{m} \times 100 = 60 \, \text{cm} \]

### Final Answer:
The wavelength of the reflected waves received by the receiver is \( 60 \, \text{cm} \).

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